A universal soil-water characteristic curve model based on the particle size distribution and fractal theory

A soil-water characteristic curve (SWCC) is a prerequisite relationship to study water transport in unsaturated soils and has significant applications in agriculture and engineering sciences. Therefore, many SWCC models were proposed and improved the understanding of water transport. Many of these models were obtained depending on the particle size distribution (PSD) because the water content is related to the sizes and distributions of particles and pores in soils. However, the continuous PSD was divided into many fractions to calculate the water content in these models. Moreover, the particles and pores were simplified as spheres and cylinders, respectively. These simplifications are idealistic and contrary to actual complex structures in soils. To solve the above limitations of these models, we considered the Weibull distribution and fractal theory and established a universal SWCC model called PF (PSD and fractal theory) based on the continuous PSD and irregularities of the pore structures. The new proposed PF model was verified by measured data in the UNSODA database. Furthermore, its accuracy was proven by comparison with two classical models widely used. The verification and comparison results show that the PF model can well describe the measured data of various types of soils and has fewer errors than the other two models. Meanwhile, the continuous PSD in this study overcomes the limitation of artificial discretization and is convenient for subsequent calculation. In addition, the actual irregular soil geometry is described by the fractal theory, which well matches complex soil structures. Therefore, the PF model based on the PSD and the fractal theory is reasonable and reliable in predicting SWCC. In addition, this study can provide a foundation and reference for subsequent studies on hydraulic behaviors.